A237800 - OEIS

%I #7 Feb 22 2014 13:21:28

%S 1,2,2,3,3,5,5,8,9,12,14,19,21,27,32,39,45,56,64,78,90,107,124,148,

%T 169,199,229,268,306,357,406,471,536,617,701,805,910,1041,1177,1341,

%U 1511,1717,1931,2187,2457,2773,3109,3503,3918,4403,4919,5514,6150,6881

%N Number of partitions of n such that 2*(least part) >= number of parts.

%e a(7) = 5 counts these partitions: 7, 61, 52, 43, 322.

%t z = 55; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := Length[p];

%t Table[Count[q[n], p_ /; 2 Min[p] < t[p]], {n, z}]   (* A237758 *)

%t Table[Count[q[n], p_ /; 2 Min[p] == t[p]], {n, z}]  (* A237757 *)

%t Table[Count[q[n], p_ /; 2 Min[p] > t[p]], {n, z}]   (* A237799 *)

%t Table[Count[q[n], p_ /; 2 Min[p] >= t[p]], {n, z}]  (* A237800 *)

%Y Cf. A237758, A118084, A237757, A237799.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Feb 15 2014